Answer:
Cost for each movie: $1.50 Cost for each video game: $6.75
Step-by-step explanation:
Let x be the cost (in dollars) of renting a movie.
Let y be the cost (in dollars) of renting a video game.
The total cost of renting 3 movies and 2 video games is +3x2y dollars.
We're given that this total cost is $18, so we have =+3x2y18.
The total cost of renting 5 movies and 6 video games is +5x6y dollars.
We're given that this total cost is $48, so we have =+5x6y48.
Therefore, we get the following system of equations.
=+3x2y18
=+5x6y48
Multiplying the first equation by −3 and adding gives us the following.
−9 x− 6 y = −54 5 x+ 6 y = 48 −4 x+ 0 y = −6
So we get the equation =−4x−6.
Solving for x, we get the following.
=x1.5
To find y, we can substitute 1.5 for x in =+3x2y18, the first equation in the system.
Then we solve for y.
+31.52y =18
+4.52y =18
2y =13.5
y =6.75
So, we have found that =x1.5 and =y6.75.
This means that the rental cost for each movie is $1.50 and the rental cost for each video game is $6.75.
